This paper is concerned with the theory of unbiased estimation for nonparametric families of distributions subject to "generalised moment" restrictions. Necessary and sufficient conditions under which symmetric statistics are unique minimum variance unbiased estimators of their expectations are obtained, and some new boundedly complete families of distributions are exhibited.
N. I. Fisher. "Unbiased Estimation for Some Non-Parametric Families of Distributions." Ann. Statist. 10 (2) 603 - 615, June, 1982. https://doi.org/10.1214/aos/1176345801